As far as coming on private property without a warrant, the police are allowed to conduct warrantless searches and seizures in a number of circumstances. The basic idea is that they may do this when there is a good reason for them to believe that a crime is being committed or that evidence of a crime is present right now but will not be present by the time they get a warrant.
So, for example, if the police hear screams coming from behind your fence, they can come and investigate since the screams would give them reasonable cause to believe a crime is being committed.
As another example, if the police think they see you selling drugs out on the street and then you disappear inside your house, they can come in without a warrant. This is because by the time they got the warrant, you could flush the drugs.
So the requirement that police have a warrant does not apply in this sort of "emergency" situation.